I travel to England twice a year and I save money by picking up "ready meals" from stores like Tesco, Marks and Spencer, and Sainsburys. (I like Marks and Spencer best). I rarely dine out. The big museums in London are free. Some have special exhibitions that cost, but they are optional. London will always be expensive but you can do your best. It helps that you are sharing expenses with a friend. Go to Airbnb and use the filters to get results in your budget. Be sure to read carefully, including in the reviews, to check how close they are to tubes, etc. I get that hostels are out of the question for you. But you might consider a shared home where it's the two of you along with the homeowner. It's a lot cheaper. I've never done it before but am considering it for next summer. You might even consider one week in London and one week outside of London in a place more affordable. Brighton is an hour away on the train. Oxford, Bath, and other historic and beautiful places might offer something for you.